Polarization measurements of an optical beam are needed for various analytic applications. Such polarization measurement techniques, often referred to as optical polarimetry, are utilized inter alia in ellipsometry, bioimaging, and imaging polarimetry.
A general polarization state of an optical beam can be defined by Stokes parameters. Stokes parameters are a set of four values describing the polarization state of an optical beam, or generally of electromagnetic radiation being coherent or incoherent radiation. Several commonly used methods for determining polarization state of an optical beam by represented Stokes parameters are based on measurement of time-dependent signal of the optical beam to transmitted through a rotating quarter-wave plate followed by a polarization analyzer. The polarization state can be determined by Fourier analysis of the detected output signal [1]. Other methods were developed aimed at providing a faster and simpler polarization measurement technique. Such methods are based on four-channel polarimeters [2] and utilize a beam splitter which divides the input beam into four channels. Each one of the split beam components is analyzed by use of different polarizing optics, and the polarization state of the input beam is calculated from the measured intensities of the four split beams. These techniques, however, suffer from a requirement for multiple polarizers and also from the fact that they can only provide polarization measurements for optical beams with uniform polarization [3].
For example, U.S. Pat. No. 5,298,972 describes an instrument including a polarized optical source for producing three sequential predetermined states of polarization of a light beam and an optical polarization meter for measuring the polarization of a portion of the light beam transmitted by or reflected from an optical network. According to this technique, the light beam is split into four beams; three of the beams pass through optical elements, and the transmitted intensity of all four beams is measured for calculating Stokes parameters. The light beam enters the optical polarization meter through a single-mode optical fiber that acts as a spatial filter for controlling the position and alignment of the beam with respect to the optical elements. The distortion of the light beam polarization caused by this optical fiber is corrected by introducing two different linearly polarized light beams and measuring Stokes parameters which are used to construct a calibration matrix that is inverted and multiplied times measured Stokes parameters of subsequent measurements to yield true Stokes parameters. The three sequential predetermined states of polarization yield three corresponding Jones input vectors, and the Stokes parameters for the responses of the optical network are converted to three Jones output vectors. A Jones matrix for the optical network to within a complex constant is then computed from the Jones input and output vectors. Relative polarization sensitivity can be determined from this matrix for the optical network. The relative distortion caused by the optical network can be corrected by multiplying by the inverse of the matrix during later measurements through the optical network. Additionally, power measurements on the optical network and proper substitutions enable absolute determinations and corrections.
U.S. Pat. No. 5,227,623 describes an instrument that includes a polarized optical source for producing three sequential predetermined states of polarization of a light beam at each of at least two wavelengths, as well as an optical polarization meter for measuring the polarization of a portion of the light beam at each wavelength transmitted by or reflected from an optical network by splitting it into four beams, passing three of the beams through optical elements, measuring the transmitted intensity of all four beams, and calculating Stokes parameters. The three sequential predetermined states of polarization at each wavelength yield three corresponding Jones input vectors at each wavelength, and the Stokes parameters for the responses of the optical network are converted to three Jones output vectors at each wavelength. A Jones matrix for the optical network to within a complex constant is then computed from the Jones input and output vectors at each wavelength. Polarization mode dispersion in the optical network is determined from these matrices.
Recently, new approaches have been developed, providing a capability for space-variant polarization profiling of an optical beam. Some of such polarimetry techniques utilize polarization gratings and a polarizer [4]. Theoretical studies and experimental demonstrations of applicability showed a use of sub-wavelength dielectric gratings [5]. Other newly developed techniques involve a use of a calcite crystal for splitting an input beam into beam components of two orthogonal polarizations. The two components, having ordinary and extra-ordinary polarizations with respect to an axis of the calcite crystal, are directed each to a different detector to obtain real-time polarization measurement [6].
U.S. Pat. No. 7,679,744 provides a Stokes parameter measurement device and Stokes parameter measurement method. The Stokes parameter measurement device comprises a polarization splitting device which comprises an optical element formed of a birefringent crystal material and which, by means of the optical element, splits signal light to be measured into a plurality of polarized light beams and adjusts the polarization state of one or more among the plurality of polarized light beams, and a light-receiving portion for performing photoelectric conversion of an optical component of the signal light split by and emitted from the polarization splitting device.
The above described polarization measurement techniques, as well as currently existing polarization measurement systems, are based on several sequential measurements combining mechanical rotation of polarization elements between one measurement to the next, and are hence expensive, complicated and slow [7].
General Description
There is a need in the art for a novel polarization measurement technique which is capable of providing, in real-time, information about the full polarization state of an optical beam, i.e. space-varying polarization and/or wavelength-varying polarization. The present invention provides a novel approach for real time determination of a space-varying polarization profile of an optical beam, i.e. technique capable of measuring polarization distribution (profile) along the cross-section of the beam. Also, the measurement is sensitive to temporal variations in the polarization state across the beam.
The technique of the present invention provides a system and method for polarization measurement of an optical beam having non-uniform polarization distribution such as radially and azimuthally polarized beam. The invention is capable of providing time-varying polarization profile of any general or randomly polarized optical beam. Optical beams having space and time varying polarization states are extremely useful in various applications such as microscopy, material processing, trapping and acceleration of particles, laser light amplifications, and polarization encryption applications.
The polarization measurement technique of the present invention is based on splitting an input optical beam into a predetermined number of substantially parallel beam components, each having a predetermined shift in the polarization state with respect to other beam components. The beam components are simultaneously detected using a pixel matrix, such as a CCD camera, to determine intensity distribution within each of the beam components. The polarization state distribution along the cross-section of the input optical beam is determined in real time according to the detected intensity distribution of the beam components utilizing determination of Stokes parameters.
The polarization state of the input optical beam can be described by distribution of Stokes parameters along the cross-section of the beam. Stokes parameters are a set of four values describing the polarization state of electromagnetic radiation, often presented as a vector (S0, S1, S2, S3). According to the invention, the Stokes parameter vector is determined for each point (image pixel) along the cross-section of the input beam in accordance with the intensity distribution across each of a predetermined number of split beam components, as detected by the pixel matrix.
The input optical beam is divided into a certain number (preferably three) beam components by a first polarization beam splitter, which is configured to impose, while splitting, a different polarization rotation on each of the split beam components. A birefringent element, for example a calcite crystal, is located in an optical path of the three split beam components and configured to further split each of these beam components into a pair of spatially separated output beam components of ordinary and extraordinary polarizations with respect to an axis of the birefringent element. The intensity distribution within each of the output beam components is detected by a pixel matrix located in an optical path of said beam components. Stokes parameters' distribution which represents the polarization distribution of the input optical beam can be determined according to the intensity distribution of the output beam components detected by the pixel matrix. A time dependent polarization state of the input beam may be determined according to the intensity distribution of the output beam components detected at a frame rate of said pixel matrix.
The invention may also provide for polarization measurement as a function of wavelength. This can be achieved by utilizing a grating in between the first polarization beam splitter and the birefringent element to spatially separate different wavelength components of the input optical beam. A narrow slit may be used being located upstream of the first polarization beam splitter in order to obtain both wavelength-dependent and one-dimensional varying polarization distribution of the input beam.
According to one broad aspect of the invention, there is provided a system for use in measuring polarization of an optical beam, wherein the system is configured and operable for determining polarization profile along a cross section of the input optical beam. The system comprises an optical system which comprises a polarization beam splitting assembly, and a pixel matrix. The polarization beam splitting assembly is configured and operable for splitting the input optical beam into a predetermined number of beam components with a predetermined polarization relation between them. The polarization beam splitting assembly comprises a first polarization beam splitter in an optical path of the input optical beam splitting the input optical beam into a first plurality of beam components with a certain polarization relation between them and a birefringent element in an optical path of the first plurality of the beam components for splitting each of them into a pair of ordinary and extraordinary polarization components, thereby producing said predetermined number of output beam components. The pixel matrix detects intensity distribution within a beam incident thereon. The pixel matrix is located in substantially non intersecting optical paths of the output beam components and generates a corresponding number of output data pieces indicative of intensity distribution within the detected output beam components, respectively. Data contained in these data pieces is indicative of the polarization profile along the cross section of the input optical beam.
The system is associated with a control unit connectable to the output of the pixel matrix and configured and operable to receive the measured data (multiple data pieces), analyze the intensity distribution within each of the output beam components, and determine Stokes parameters of the input optical beam which are indicative of the polarization profile of the beam.
Preferably, the system produces six output beam components. The first polarization beam splitter is configured and operable to produce from the input optical beam three spatially separated beam components of different polarizations.
The determined polarization profile may correspond to space and time variant of polarization components within the cross-section of the input optical beam.
In some embodiments of the invention, the first polarization beam splitter comprises first and second reflective surfaces accommodated in a spaced-apart substantially parallel planes intersecting with an optical axis of light propagation through the system. The first reflective surface is partially reflective and has a segment thereof located in the optical path of the input optical beam thereby splitting said input optical beam into a first portion transmitted through said first polarization beam splitter towards the birefringent element and a second portion reflected towards the second reflective surface. The second reflective surface is relatively highly reflective and reflects said second beam portion towards a segment of the first reflective surface. The first and second reflective surfaces thereby operate together to sequentially reflect and split portions of said input optical beam into said first plurality of beam components propagating along spatially separated optical paths to the birefringent element.
In some embodiments of the invention, the first polarization beam splitter comprises an optically transparent plate having first and second parallel sides at least partially coated with reflective coatings defining said first and second reflective surfaces. The first sides of the optically transparent plate is coated to provide partially reflective surface and has a segment thereof located in the optical path of the input optical beam thereby splitting said input optical beam into a first portion transmitted through said first polarization beam splitter towards the birefringent element and a second portion reflected towards the second reflective surface. The second opposite side of the optically transparent plate comprises a segment which is coated to provide high reflective surface. The first and second coated surfaces of said optically transparent plate thereby operate to sequentially reflect and split portions of said input optical beam into said first plurality of beam components propagating along spatially separated optical paths to the birefringent element. In some other embodiments, the first and second reflective surfaces are constituted by separate spaced-apart elements (mirrors).
In some embodiments, the first and second surfaces are located in the planes forming a predetermined angle with the optical axis, thereby causing polarization rotation of beam components interacting with said first and second surfaces, thereby producing said predetermined polarization relation between the beam components in said first plurality. This may be a 88 degrees angle, or 33 degrees angle. In some other embodiments, the first polarization beam splitter comprises a polarization rotator located between said first and second reflective surfaces (e.g. a quarter wave plate oriented at an angle with respect to the optical axis) to thereby provide said polarization relation between the beam components emerging from the first polarization beam splitter towards the birefringent element. In either of these embodiments, the beam interactions with the first polarization beam splitter results in an optical delay between polarization components of each interacting beam component, thus actually inducing polarization rotation and thus polarization difference between each two locally adjacent beam components emerging from the first polarization beam splitter. For example, the optical delay of λ/4 corresponds to π/2 phase difference between the polarization components of the beam.
In some embodiments, the system comprises a grating located between the first polarization beam splitter and the birefringent element, and configured to diffract different wavelengths of the input optical beam. Preferably, a focusing lens assembly is located in the optical path of the beam components propagating from the grating to the birefringent element. Also, the system may include a slit (aperture) located in an optical path of the input optical beam.
According to another broad aspect of the invention, there is provided an optical device for use in a measurement of polarization profile along a cross section of an optical beam, the optical device comprising: a polarization beam splitting assembly configured and operable for splitting an optical beam into six beam components with a predetermined polarization relation between them, the polarization beam splitting assembly comprising a first polarization beam splitter in an optical path of said optical beam configured for splitting said optical beam into three spatially separated beam components with a certain polarization relation between them propagating along three spaced-apart substantially parallel optical paths, and a birefringent element located in said optical paths for splitting each of said three beam components into a pair of ordinary and extraordinary polarization components, thereby producing said six beam components; intensity distribution within of said six beam components of the optical beam being indicative of the polarization profile along the cross section of said optical beam.
According to yet further aspect of the invention, there is provided a method for use in measuring polarization of an optical beam, the method comprising: splitting the optical beam into three pairs of beam components with a predetermined polarization relation between the pairs, each pair comprising ordinary and extraordinary polarization components, measuring intensity distribution within each of said six beam components, analyzing the intensity distributions of the six beam components and determining a polarization profile along a cross section of the optical beam.